NAME ____________________________ DATE ________________ CLASS __________________
Two-Dimensional Motion and Vectors
Problem B
RESOLVING VECTORS
PROBLEM
Certain iguanas have been observed to run as fast as 10.0 m/s. Suppose an iguana
runs in a straight line at this speed for 5.00 s. The direction of motion makes an angle
of 30.0 to the east of north. Find the value of the iguana’s northward displacement.
SOLUTION
1. DEFINE
Given:
v = 10.0 m/s
t = 5.00 s
 = 30.0
Unknown: y = ?
Diagram:
2. PLAN Choose the equation (s) or situation: The northern component of the
vector is equal to the vector magnitude times the cosine of the angle between the
vector and the northward direction.
y = d(cos )
Use the equation relating displacement with constant velocity and time, and
substitute it for d in the previous equation.
d = vt
y = vt(cos )
3. CALCULATE Substitute the values into the equation (s) and solve:

m 
y  10.0 (5.00 s)(cos 30.0)
s 

 43.3 m, north
4. EVALUATE
The northern component of the displacement vector is smaller
than the displacement itself, as expected.

ADDITIONAL PRACTICE
1. A common flea can jump a distance of 33 cm. Suppose a flea makes five
jumps of this length in the northwest direction. If the flea’s northward
displacement is 88 cm, what is the flea’s westward displacement?
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
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Problem Workbook
NAME ____________________________ DATE ________________ CLASS __________________
2. The longest snake ever found was a python that was 10.0 m long. Suppose a
coordinate system large enough to measure the python’s length is drawn on the
ground. The snake’s tail is then placed at the origin and the snake’s body is
stretched so that it makes an angle of 60.0 with the positive x-axis. Find the
x and y coordinates of the snake’s head. (Hint: The y-coordinate is positive.)
3. A South-African sharp-nosed frog set a record for a triple jump by traveling a
distance of 10.3 m. Suppose the frog starts from the origin of a coordinate
system and lands at a point whose coordinate on the y-axis is equal to 6.10 m.
What angle does the vector of displacement make with the negative y-axis?
Calculate the x component of the frog.
4. The largest variety of grasshopper in the world is found in Malaysia. These
grasshoppers can measure almost a foot (0.305 m) in length and can jump
4.5 m. Suppose one of these grasshoppers starts at the origin of a coordinate
system and makes exactly eight jumps in a straight line that makes an angle of
35 with the positive x-axis. Find the grasshopper’s displacements along the
x- and y-axes. Assume both component displacements to be positive.
5. The landing speed of the space shuttle Columbia is 347 km/h. If the shuttle is
landing at an angle of 15.0 with respect to the horizontal, what are the
horizontal and the vertical components of its velocity?
6. In Virginia during 1994 Elmer Trett reached a speed of 372 km/h on his
motorcycle. Suppose Trett rode northwest at this speed for 8.7 s. If the angle
between east and the direction of Trett’s ride was 60.0, what was Trett’s
displacement east? What was his displacement north?
7. The longest delivery flight ever made by a twin-engine commercial jet took
place in 1990. The plane covered a total distance of 14 890 km from Seattle,
Washington to Nairobi, Kenya in 18.5 h. Assuming that the plane flew in a
straight line between the two cities, find the magnitude of the average velocity
of the plane. Also, find the eastward and southward components of the average
velocity if the direction of the plane’s flight was at an angle of 25.0 south of
east.
8. The French bomber Mirage IV can fly over 2.3  103 km/h. Suppose this plane
accelerates at a rate that allows it to increase its speed from 6.0  102 km/h to
2.3  103 km/h in a time interval of 120 s. If this acceleration is upward and at
an angle of 35 with the horizontal, find the acceleration’s horizontal and
vertical components.
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
Holt Physics
20
Problem Workbook